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range operator
>< Cartesian product ?, Man search online help system Abs absolute value of a number Adjoint adjoint matrix Alias define aliases for package names Alias In temporarily override global aliases Aliases list of global aliases Append append an object to an existing list Ascii convert between characters and ascii code Bin binomial coefficient BinExp, EvalBinExp binomial expansion Block group several commands into a single command BlockMatrix create a block matrix Break break out of a loop BringIn bring in objects from another ring Call apply a function to given arguments Cast type conversion Catch catch an error CFApprox, CFApproximants, ContFrac continued fractions Characteristic the characteristic of a ring Ciao quit CoCoA Clear clear the working memory or a ring-bound memory Close close a device CocoaLimits limits on exponents and ring characteristics CocoaPackagePath returns the path to the CoCoA packages Coefficients list of coefficients of a polynomial or vector CoeffOfTerm coefficient of a term of a polynomial or vector Colon, :, HColon ideal or module quotient ColumnVectors the list of column vectors of a matrix Comp the N-th component of a list Comps list of components of a vector Concat, ConcatLists concatenate lists or lists of lists, respectively Cond conditional expression Contrib list of contributors to CoCoA Count count the objects in a list CurrentRing the current ring Dashes returns string of dashes Date the date DecimalStr convert rational number to decimal string Define define a function Defined check if an expression has been defined Deg the degree of a polynomial or vector DegLexMat, DegRevLexMat, LexMat, XelMat matrices for std. term-orderings Delete delete variables from the working memory DensePoly the sum of all power-products of a given degree Der the derivative of a rational function Describe information about an expression Destroy delete rings Det the determinant of a matrix Diff returns the difference between two lists Dim the dimension of a ring or quotient object Discriminant the discriminant of a polynomial Distrib the distribution of objects in a list Div, Mod quotient and remainder for integers DivAlg division algorithm E_ canonical vector Elim eliminate variables EqSet checks if the set of elements in two lists are equal Equals returns a string of equal signs EquiIsoDec equidimensional isoradical decomposition Error return an error message Eval substitute numbers or polynomials for indeterminates EvalHilbertFn evaluate the Hilbert function Fact factorial function Factor factor a polynomial Fields list the fields of a record First the first N elements of a list FirstNonZero, FirstNonZeroPos the first non-zero entry in a vector Flatten flatten a list FloatApprox approx. of rational number of the form M*10^E FloatStr, MantissaAndExponent convert rational number to a float string For loop command Foreach loop command Format convert object to formatted string Fraction returns the quotient of its arguments Function return a function Functions list the functions of a package GB.Complete Complete an interactive Groebner-type calculation GB.GetBettiMatrix returns the Betti matrix computed so far GB.GetNthSyz returns the part of the Nth syzygy module computed so far GB.GetNthSyzShifts shifts of the Nth syzygy module computed so far GB.GetRes returns the resolution computed so far GB.GetResLen returns the length of the resolution computed so far GB.ResReport status of an interactive resolution calculation GB.Start_GBasis start interactive Groebner basis computation GB.Start_MinGens start interactive minimal generator calculation GB.Start_MinSyzMinGens start interactive calc., min. syzs. of min. gens. GB.Start_Res start interactive resolution computation GB.start_Syz start interactive syzygy computation GB.start_SyzMinGens start interactive calc. of syzygies of min. gens. GB.Stats status of an interactive Groebner-type calculation GB.Step, GB.Steps take steps in an interactive Groebner-type calculation GBasis calculate a Groebner basis GBM, HGBM intersection of ideals for zero-dimensional schemes GCD, LCM greatest common divisor, least common multiple GenericPoints random projective points GenRepr representation in terms of generators Gens list of generators of an ideal Get read characters from a device GetErrMesg returns the message associated with an error Gin generic initial ideal GlobalMemory contents of global memory H.Browse browse the online help system H.Commands list commands according to type H.Man search online help system (see "?, Man") H.OutCommands print command descriptions to a file H.OutManual print the online manual to a file H.SetMore, H.UnSetMore more-device for online help H.Syntax display the syntax of a command H.Tips quick tips for using online help H.Toc display the Table Of Contents of the online manual H.Tutorial run the CoCoA tutorial Head the first element of a list Help extend online help for user-defined functions Hilbert the Hilbert function HilbertBasis Hilbert basis for a monoid HilbertPoly the Hilbert polynomial HIntersection, HIntersectionList intersection of ideals Homogenized homogenize with respect to an indeterminate HVector the h-vector of a ring or quotient object Ideal convert an expression into an ideal IdealAndSeparatorsOfPoints ideal and separators for affine points IdealAndSeparatorsOfProjectivePoints ideal and separators for points IdealOfPoints ideal of a set of affine points IdealOfProjectivePoints ideal of a set of projective points Identity the identity matrix If conditional statement ILogBase integer part of the logarithm Image ring homomorphism In create a list satisfying given conditions Indet individual indeterminates IndetInd the index of an indeterminate IndetIndex index of an indeterminate IndetName the name of an indeterminate Indets list of current indeterminates Insert, Remove insert or remove an object in a list Interpolate interpolating polynomial Interreduce, Interreduced interreduce a list of polynomials or vectors Intersection, IntersectionList intersect lists, ideals, or modules Inverse multiplicative inverse IO.SprintTrunc convert to a string and truncate Iroot integer part of r-th root of an integer IsEven, IsOdd test whether an integer is even or odd IsHomog test whether given polynomials are homogeneous IsIn check if one object is contained in another IsNumber checks if the argument is a number IsPosTo, IsToPos checks the module term-ordering of a ring IsPrime prime integer test Isqrt computes the (truncated) square root of an integer IsStable, IsStronglyStable, IsLexSegment checks if an ideal is stable (resp. strongly stable or a lex-segment) IsSubset checks if the elements of one list are a subset of another IsTerm checks if the argument is a term IsZero test whether an object is zero Jacobian the Jacobian of a list of polynomials Last the last N elements of a list Latex LaTeX formatting LC the leading coefficient of a polynomial or vector Len the length of an object LinKer find the kernel of a matrix LinSol find a solution to a linear system List convert an expression into a list LM the leading monomial of a polynomial or vector Log the list of exponents of the leading term of a polynomial LogToTerm returns a monomial (power-product) with given exponents LPos the position of the leading power-product in a vector LPP the leading power-product of a polynomial or vector LT the leading term of an object MapDown convert a constant polynomial to a number Mat convert an expression into a matrix Max, Min a maximum or minimum element of a sequence or list MDeg multi-degree of an polynomial Memory contents of local memory or ring-bound memory MinGens list minimal generators Minimalize, Minimalized remove redundant generators Minors list of minor determinants of a matrix MinSyzMinGens minimal generators of syzygies of minimal generators Mod2Rat reconstructing rationals from modular integers Module convert an expression into a module Monic divide polynomials by their leading coefficients Monomials the list of monomials of a polynomial or vector MonsInIdeal ideal generated by the monomials in an ideal More print a string, N lines at a time Multiplicity the multiplicity (degree) of a ring or quotient object NewId create a new identifier NewList create a new list NewMat create a new matrix NewVector create a new vector NextPrime find the next largest prime number NF normal form NFsAreZero test if normal forms are zero NonZero remove zeroes from a list Not, And, Or boolean operators NR normal reduction Num, Den numerator, denominator NumComps the number of components of a vector NumIndets number of indeterminates OpenIFile, OpenOFile open input or output file OpenIString, OpenOString open input or output string OpenLog, CloseLog open or close a log of a CoCoA session Option status of a panel option Ord matrix defining a term-ordering Packages list of loaded packages Panel print status of a panel's options Panels list of CoCoA panels Partitions partitions of an integer Pfaffian the Pfaffian of a skew-symmetric matrix PkgName returns the name of a package Poincare, HilbertSeries the Poincare series Poly convert an expression into a polynomial PrimaryDecomposition primary decomposition of an ideal Print On print to an output device Print, PrintLn print the value of an expression Product, Sum the product or sum of the elements of a list Quit quit CoCoA QuotientBasis vector space basis for zero-dimensional quotient rings QZP, ZPQ change field for polynomials and ideals Radical radical of an ideal RadicalOfUnmixed radical of an unmixed ideal Rand random integer Randomize, Randomized randomize the coefficients of a given polynomial Rank rank of a module RealRootRefine refine a root of a univariate polynomial over Q RealRoots computes a root of a univariate polynomial over Q Record create a record ReducedGBasis compute a reduced Groebner basis Repeat loop command Res free resolution Reset reset panels and random number seed to defaults ResetPanels reset panels to their default values Resultant the resultant of two polynomials Return exit from a structured command Reverse, Reversed reverse a list Ring returns the ring with a given name RingEnv name of the current ring RingEnvs names of all defined rings RootBound bound on roots of a polynomial over Q Saturation, HSaturation saturation of ideals ScalarProduct scalar product Seed seed for Rand
SeparatorsOfPoints separators for affine points SeparatorsOfProjectivePoints separators for projective points Set remove duplicates from a list Set, Unset set and unset panel options Shape extended list of types involved in an expression Size the amount of memory used by an object Skip does nothing Sort, Sorted sort a list SortBy, SortedBy sort a list Source, << read commands from a file or device Spaces return a string of spaces Sprint convert to a string StarPrint print polynomial with *'s for multiplications Starting list functions starting with a given string Submat submatrix Subsets returns all sublists of a list Subst substitute values for indeterminates Support the list of terms of a polynomial or vector Sylvester the Sylvester matrix of two polynomials Syz syzygy modules SyzMinGens syzygy module for a set of minimal generators SyzOfGens syzygy module for a given set of generators Tag returns the tag string of an object Tagged, Untagged, @ tag or untag an object for pretty printing Tail remove the first element of a list TensorMat returns the tensor product of two matrices Toric saturate toric ideals Toric.CheckInput check input to Toric
Transposed the transposition of a matrix Tuples N-tuples Type the data type of an expression TypeOfCoeffs type of the coefficients of the current ring Types lists all data types Use command for making a ring active Using perform commands in non-active ring Var function calls by reference, other complex referencing Vector create a vector WeightsList first row of the weights matrix WeightsMatrix matrix of generalized weights for indeterminates While loop command WithoutNth removes the N-th component from a list WLog weighted list of exponents |